MODELING, STABILITY ANALYSIS AND CONTROL OF MICROGRID. A Thesis submitted in Partial Fulfilment of the Requirement for the Degree of Doctor of Philosophy Ritwik Majumder M.Sc (Engg), B.E (Electrical engineering) Faulty of Build and Environment Engineering School of Engineering Systems Queensland University of Technology Queensland, Australia February 2010
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MODELING, STABILITY ANALYSIS AND CONTROL OF MICROGRID.
A Thesis submitted in Partial Fulfilment of the Requirement for the
Degree of
Doctor of Philosophy
Ritwik Majumder
M.Sc (Engg), B.E (Electrical engineering)
Faulty of Build and Environment Engineering
School of Engineering Systems
Queensland University of Technology
Queensland, Australia
February 2010
KEYWORDS
Microgrid Distributed Generators Islanding Resynchronization Voltage Source Converter Converter Structure and Control Voltage Control State Feedback Control Power Sharing Droop Control Frequency Droop Angle Droop Power Quality Back to Back Converters Stability Rural Distributed Generation Modified Droop Control Web Based Communication
ABSTRACT
With the increase in the level of global warming, renewable energy based
distributed generators (DGs) will increasingly play a dominant role in electricity
production. Distributed generation based on solar energy (photovoltaic and solar
thermal), wind, biomass, mini-hydro along with use of fuel cells and micro turbines
will gain considerable momentum in the near future. A microgrid consists of clusters
of load and distributed generators that operate as a single controllable system. The
interconnection of the DG to the utility/grid through power electronic converters has
raised concern about safe operation and protection of the equipments.
Many innovative control techniques have been used for enhancing the
stability of microgrid as for proper load sharing. The most common method is the use
of droop characteristics for decentralized load sharing. Parallel converters have been
controlled to deliver desired real power (and reactive power) to the system. Local
signals are used as feedback to control converters, since in a real system, the distance
between the converters may make the inter-communication impractical. The real and
reactive power sharing can be achieved by controlling two independent quantities,
frequency and fundamental voltage magnitude.
In this thesis, an angle droop controller is proposed to share power amongst
converter interfaced DGs in a microgrid. As the angle of the output voltage can be
changed instantaneously in a voltage source converter (VSC), controlling the angle
to control the real power is always beneficial for quick attainment of steady state.
Thus in converter based DGs, load sharing can be performed by drooping the
converter output voltage magnitude and its angle instead of frequency. The angle
control results in much lesser frequency variation compared to that with frequency
droop.
An enhanced frequency droop controller is proposed for better dynamic
response and smooth transition between grid connected and islanded modes of
operation. A modular controller structure with modified control loop is proposed for
better load sharing between the parallel connected converters in a distributed
generation system. Moreover, a method for smooth transition between grid
connected and islanded modes is proposed.
Power quality enhanced operation of a microgrid in presence of unbalanced
and non-linear loads is also addressed in which the DGs act as compensators. The
compensator can perform load balancing, harmonic compensation and reactive
power control while supplying real power to the grid
A frequency and voltage isolation technique between microgrid and utility is
proposed by using a back-to-back converter. As utility and microgrid are totally
isolated, the voltage or frequency fluctuations in the utility side do not affect the
microgrid loads and vice versa. Another advantage of this scheme is that a
bidirectional regulated power flow can be achieved by the back-to-back converter
structure.
For accurate load sharing, the droop gains have to be high, which has the
potential of making the system unstable. Therefore the choice of droop gains is often
a tradeoff between power sharing and stability. To improve this situation, a
supplementary droop controller is proposed. A small signal model of the system is
developed, based on which the parameters of the supplementary controller are
designed.
Two methods are proposed for load sharing in an autonomous microgrid in
rural network with high R/X ratio lines. The first method proposes power sharing
without any communication between the DGs. The feedback quantities and the gain
matrixes are transformed with a transformation matrix based on the line R/X ratio.
The second method involves minimal communication among the DGs. The converter
output voltage angle reference is modified based on the active and reactive power
flow in the line connected at point of common coupling (PCC). It is shown that a
more economical and proper power sharing solution is possible with the web based
communication of the power flow quantities.
All the proposed methods are verified through PSCAD simulations. The
converters are modeled with IGBT switches and anti parallel diodes with associated
snubber circuits. All the rotating machines are modeled in detail including their
dynamics.
CONTENTS
List of Figures xv
List of Tables xix
List of Principle Symbols xxi
1 Introduction 1 1.1 Power Sharing In Distributed Generation 2
1.2 Microgrid And Its Autonomous Control 2
1.2.1 Controls for Grid and Island Operation 4
1.3 Power Quality And Reliability 4
1.4 System Stability 6
1.5 Power Sharing In Rural Network 7
1.6 Objectives of the Thesis and Specific Contributions 8
1.6.1 Objectives of the Thesis 8
1.6.2 Specific Contributions of the Thesis 9
1.7 Thesis Organization 10
2 Power Sharing with Converter Interfaced Sources 13 2.1 Control Of Parallel Converters For Load Sharing With
Frequency Droop 13
2.1.1 Frequency Control 14
2.1.2 Modular Control Structure 14
2.1.3 Converter Voltage Angle Calculation 15
2.1.4 Reference Generation 15
2.2 Angle Droop Control 17
2.2.1 Angle Droop Control And Power Sharing 18
2.3 Angle Droop And Frequency Droop Controller 20
2.4 Simulation Studies 22 2.4.1 Frequency Droop Controller 22
2.4.2 Angle Droop Controller 23 2.4.3 Comparison Of Frequency Droop And Angle Droop 23 2.4.4 Angle Droop In Multi DG System 25
2.5 Conclusions 27
3 Load Frequency Control in Microgrid 28 3.1 Seamless Transfer between Grid Connected and Islanded Modes 28 3.2 Proposed Control 29
3.3 Simulation Studies 30
x
3.3.1 Islanded Mode 30
3.3.2 Grid Connected Mode 32
3.3.3 Seamless Transfer Between Grid Connected
and Islanded Modes 33
3.4 Microgrid with Inertial and Non Inertial DGs 37
3.4.1 System Structure 38
3.4.2 Micro Source Model 38
3.4.2.1 Fuel Cell 38
3.4.2.2 Photo Voltaic Cell (PV) 39
3.4.2.3 Battery 39
3.4.3 Simulation Studies 40
3.4.3.1 Case 1: Grid Connected and Autonomous Operating Modes 40
3.4.3.2 Case 2: Power Sharing In Autonomous Mode 40
3.4.3.3 Case 3: Source Inertia And System Damping 41
3.5 Conclusions 42
4 Power Quality Enhanced Operation of a Microgrid 44 4.1 System Structure 45
4.2 Reference Generation And Compensator Control 46
4.2.1 Compensator Reference Generation in Grid
Connected Mode 46
4.2.2 Compensator Control 50
4.2.3 Compensator Reference Generation in Islanded Mode 51
4.2.4 DG Coordination for Sharing the Common Load 52
4.3 Simulation Studies 54
4.3.1 Sharing the Local Load with Utility 54
4.3.2 Sharing the Common Load by The DGs 56
4.3.3 Sharing a Common Induction Motor Load 57
4.3.4 DG-1 Supplying the Entire Common Load during Islanding 58
4.4 Discussions 59
4.5 Conclusions 60
5 Power Flow Control with Back-to Back Converters in a Utility Connected Microgrid 65 5.1 System Structure and Operation 65
5.5 Relay and Circuit Breaker Coordination during Islanding and Resynchronization 72
5.6 Simulation Studies 74
5.6.1 Case-1: Load Sharing of the DGs with Utility 74
5.6.2 Case-2: Change in Power Supply from Utility 76
5.6.3 Case-3: Power Supply from Microgrid to Utility 77
5.6.4 Case-4: Load Sharing with Motor Load 78
5.6.5 Case-5: Change in Utility Voltage and Frequency 79
5.6.6 Case-6: Islanding and Resynchronization 81
5.6.7 Case-7: Variable Power Supply from Utility 81
5.6.8 Case-8: DC Voltage Fluctuation and Loss of A DG 83
5.7 Microgrid Containing Multiple DGs 84
5.8 Conclusions 85
6 Stability Analysis of Multiple Converter Based Autonomous Microgrid 87 6.1 Converter Structure and Control 87
6.2 Droop Control and DG Reference Generation 88
6.2.1 Droop Control 88
6.2.2 DG Reference Generation 88
6.3 State Space Model of Autonomous Microgrid 89
6.3.1 Converter Model 90
6.3.2 Droop Controller 93
6.3.3 Combined Converter-Droop Control Model 94
6.3.4 Transformation to Common Reference Frame 95
6.3.5 Network and Load Modeling 97
6.3.6 Complete Microgrid Model 98
6.4 System Structure and Model of Autonomous Microgrid Example 99
6.5 Eigenvalue Analysis of Microgrid 101
6.6 Simulation Studies 104
6.6.1 Case 1: Full System of Fig. 6.2 (3 DG And 3 Loads) 105
6.6.2 Case 2: The Effect of System Reduction 105
6.7 Improvement in Stability with Supplementary Droop Control 107
6.7.1 Test System 110
6.7.2 Simulation Studies with Supplementary Droop Controller 110
xii
6.7.2.1 Case 1: Full System Of Fig. 6 With Lower Droop Gains 110
6.7.2.2 Case 2: Reduced System with Lower Droop Gains 111
6.7.2.3 Case 3: System Stability with High Droop Gain 112
6.7.2.4 Case 4: Power Sharing with The Proposed Supplementary Controller 113
6.7.2.5 Case 5: Power Sharing with the Proposed Controller in Reduced System 113
6.8 Conclusions 115
7 Droop Control of Converter Interfaced Micro Sources in Rural Distributed Generation 117 7.1 Power Sharing with Angle Droop and Proposed Droop Control 117
7.1.1 Proposed Controller-1 without Communication 119
7.1.2 Proposed Controller-2 with Minimum Communication 121
7.1.3 Multiple DG System 122
7.1.4 Web Based Communication 124
7.2 Converter Structure and Control 125
7.2.1 Converter Control 125
7.2.2 DG Reference Generation 126
7.3 Simulation Studies 128
7.3.1 Case 1: Load_3 and Load_4 Connected to Microgrid 128
7.3.2 Case 2: DG-1 and DG-3 Supply Load_1 and Load_2 130
7.3.3 Case 3: Induction Motor Loads 131
7.3.4 Case 4: Load Sharing with Advanced Communication System 132
7.3.5 Case 5: Load Sharing with Conventional Droop Controller 133
7.3.6 Case 6: Load Sharing With Conventional Droop Controller 134
7.4 Conclusions 134
8 Conclusions 137 8.1 General Conclusions 137
8.2 Scope for Future Work 138
Appendix-A: Converter Structure and Control 139 A.1 Converter Structure 139
A.2 Converter Control 139
A.3 Output Feedback Voltage Controller 140
A.4 State Feedback Controller 142
Appendix-B: List of Publication 145
xiii
References 149
xiv
xv
LIST OF FIGURES
2.1. Microgrid system under consideration
2.2. The modular control structure
2.3. Voltage angle control loop
2.4. Converter structure
2.5. Equivalent circuit of one phase of the converter
2.6. Source angle extraction from rotating angle
2.7 DG connection to microgrid
2.8 System stability as function of frequency droop gain
2.9 System stability as function of angle droop gain
2.10 DG power output with frequency droop control
2.11 DG power output with angle droop control
2.12 Frequency variation with frequency droop control
2.13 Frequency variation with angle droop control
2.14 Angle variation with angle droop control
2.15 Microgrid Structure with multiple DGs
2.16 Real Power Sharing of the DGs
2.17 Real Power Sharing of the DG-1 and DG-4
3.1 Microgrid system under consideration
3.2 System response with impedance load in islanded mode
3.3 System response with motor load in islanded mode
3.4 System response with impedance load in grid connected mode
3.5 System response with induction motor load in grid connected mode
3.6 System response with synchronous motor load in grid connected mode
3.7 System response during islanding and resynchronization with impedance load
3.8 PCC voltage during islanding and resynchronization with impedance load
3.9 System response during islanding and resynchronization with motor load
3.10 PCC voltage during islanding and resynchronization with motor load
3.11 DG connection to microgrid
3.12 Microgrid system
3.13 Single-phase equivalent circuit of VSC
3.14 System stability as function of frequency droop gain
3.5 System stability as function of angle droop gain
3.6 DG power output with angle droop control
3.7 Frequency variation with angle droop control
3.8 DG power output with frequency droop control
3.9 Frequency variation with frequency droop control
3.10. Microgrid structure under consideration
3.11 Fuel cell modeled equivalent circuit
xvi
3.12 Equivalent circuit of PV and boost chopper based on MPPT
3.13 MPPT control flowchart for PV
3.14 Islanding and resynchronization
3.15 Real power sharing of the DGs
3.16 Current output of the micro sources
3.17 Real power sharing of the DGs
3.18 Real power sharing of the DGs
4.1 The microgrid and utility system under consideration
4.2 Equivalent circuit of one phase of the converter
4.3 Real and reactive power sharing in DG-1and DG-2
4.4 Voltages at the PCC1 and PCC2
4.5 Power sharing and DG-1current and PCC1 voltages
4.6 Real power sharing by DG-1 and DG-2
4.7 Common load sharing between DG-1 and DG-2
4.8 Real power sharing of the DGs and voltages at PCC1 and PCC2
4.9 Microgrid structure with large number of DGs and loads
5.1 The microgrid and utility system under consideration
5.2 Angle controller for VSC-1
5.3 Schematic diagram of VSC-2 connection to microgrid
5.4 Power flow from DG-1 to microgrid
5.5 Logic for breaker operation and converter blocking
5.6 Breakers and converter blocking timing diagram
5.7 Real and reactive power sharing for Case-1
5.8 Voltage tracking of DG-1 Case-1.
5.9 Capacitor voltage and angle controller output for Case-1
5.10 Real and reactive power sharing for Case-2
5.11 Three phase PCC voltage and injected current for Case-2
5.12 Real and reactive power sharing during power reversal (Case-3)
5.13 PCC voltage and injected current for Case-3
5.14 Real and reactive power sharing with motor load (Case-4)
5.15 Real and reactive power during frequency fluctuation (Case-5)
5.16 Real and reactive power during voltage sag (Case-5)
5.17 DC capacitor voltage and angle controller output during voltage sag
5.18 Location of the single line to ground fault
5.19 DC capacitor voltage and angle controller output during islanding and resynchronization (Case-6)
5.20 Real and reactive power during islanding and resynchronization (Case-6)
5.21 Real power sharing during power limit and mode change (Case-7)
5.22 DC voltage fluctuation in DG-1 and its tripping (Case-8)
5.23 Microgrid structure with large number of DGs and loads
xvii
5.24 Real power sharing with four DGs
6.1 Interconnection diagram of the complete microgrid system
6.2 Microgrid system under consideration
6.3 Eigenvalues for nominal operating condition
6.4 Eigenvalue locus with real power droop gain change
6.5 Eigenvalue locus with reactive power droop gain change
6.6 Eigenvalue locus without DG-3
6.7. Real and reactive power during a change in load 1
6.8 Unstable operation with m = 8.18×10−5 rad/W
6.9 Marginally stable operation with n = 2.5×10−3 V/VAr
6.10 System response 3 and 2 DGs for m = 6.18×10−5 rad/W
6.11 System response for different system configuration
6.15 Real and reactive power during a change in load 1
6.16 Power sharing with reduced system
6.17 System stability with high droop gain
6.18 Power sharing with proposed controller
6.19 Droop controller and supplementary controller output
6.20 System response for different system configuration
6.21 Power sharing in reduced system
7.1 Power sharing with angle droop
7.2 Power sharing in resistive-inductive line
7.3 Multiple DG connected to microgrid
7.4 (a) Web based PQ monitoring scheme and (b) web based communication for DG-1
7.5 Power sharing with conventional controller (Case 1)
7.6 Power sharing with Controller-1 (Case 1)
7.7 Power sharing with Cntroller-2 (Case 1)
7.8 Power sharing with conventional controller (Case 2)
7.9 Power sharing with Controller-1 (Case 2)
7.10 Power sharing with Controller-2 (Case 2)
7.11 Power sharing with conventional controller (Case 3)
7.12 Power sharing with Controller-1 (Case 3)
7.13 Power sharing with Controller-2 (Case 3)
7.14 Power sharing with high bandwidth communication (Case 4)
7.15 Error in power sharing with different control techniques
7.16 Frequency droop and angle droop
7.17. Power sharing with frequency droop Case 1
7.18. Frequency dependent load
xviii
xix
LIST OF TABLES
2.1 System and Controller Parameters
2.2 Microgrid System and Controller Parameters
3.1 System Parameters
4.1 System Parameters
4.2 Numerical Results
5.1 System and controller parameters
6.1 Nominal System Parameters
6.2 Mode participation factors
6.3 Parameters of the supplementary droop control loop
6.4 Nominal System Parameters
7.1 Nominal System Parameters
7.2 Simulation Results
xx
xxi
LIST OF PRINCIPLE SYMBOLS vsa, vsb, vsc Source voltages of phases a, b, and c respectively
isa, isb, isc Source current of phases a, b, and c respectively
vPCCa, vPCCb, vPCCC PCC voltages of phases a, b, and c respectively
i1a, i1b, isc Converter current of phases a, b, and c respectively
Rs, Ls Feeder resistance and inductance respectively in utility
XD Line reactance
RD Line resistance
Cf Filter capacitance
L1, L2, L3 Filter inductance
Lf Transformer leakage reactance
Rf Transformer and VSC losses
VDC1, VDC2, VDC3 DC voltage source of the Distributed Generators
u Converter switching function
ωs Synchronous frequency
V Magnitude of converter output voltage
Angle of converter output voltage
VP Magnitude of PCC voltage
P Angle of PCC voltage
vcf Voltage across filter Capacitor
icf Current through filter Capacitor
ω Operating frequency
ωS Cut off frequency of low pass filter
P1, P2 Real power injected by DGs to microgrid
Q1, Q2 Reactive power injected by DGs to microgrid
Prated, Qrated Real and reactive power rating of the DG
Pg Real power injected by utility to microgrid
Qg Reactive power injected by utility to microgrid
PL, QL Real and reactive load power
PLC, QLC Real and reactive power of common load
1P, 1Q Real and reactive power sharing ratio with utility
m, n Droop coefficients
K State feedback controller gain
S, R Polynomials in pole shift controller
Pole shift factor
Z-1 Delay operator
h Hysteresis band
KP, KI Proportional and integral gain constant
xxii
xxiii
STATEMENT OF ORIGINAL AUTHORSHIP
The work contained in this thesis has not been previously submitted to meet requirements for an award at this or any other higher education institution. To the best of my knowledge and belief, the thesis contains no material previously published or written except where due reference is made.
First and foremost I offer my gratitude to my supervisors, Prof. Arindam Ghosh, Prof. Gerard Ledwich and A/Prof. Firuz Zare, who have supported me throughout my doctoral research. It was a great honor for me to pursue my research under their supervision.
I would like to thank Australia for giving me the opportunity of doctoral research here. I thank Queensland University of Technology and Australia Research Council (ARC) for the financial support.
I thank Saikat da, Rajat, Sachin, Ali, Arash, Jaffar, Manjula and all for the technical and much needed non technical discussions. Rajat gave me a warm welcome to Australia and without his presence, this Ph.d in QUT would not have started.
With many other staff in QUT, I would like to thank our research office (Diane and her team), theme coordinator (Christine), School Office (Noelene) for all the support and help.
Life has been always bigger than science. I thank Kie for showing me the power of simplicity and honesty in life. I thank my parents for their support and unconditional love.
xxvi
1
CHAPTER 1
The concern for climate change is driving major changes in electricity generation and
consumption patterns. Various countries have set a target of 20 % greenhouse gas reduction by the
year 2020.
Large scale changes in both transmission and distribution levels are expected to occur in the
near future. Transmission systems will be bolstered to transmit power generated from large windfarm,
geothermal and solar thermal generations.
In distribution levels, many smaller renewable generators (e.g. photovoltaic, fuel cells, micro
hydro etc.) will be connected to the networks. These are called distributed generators (DGs) or
distributed energy resources (DERS). Their integration into distributions systems disturbs the radial
nature of power flow through distribution feeders.
The interconnection of DG to the utility/grid through power electronic converters has raised
concern about safety and protection. IEEE P1547 standard [1] provides the technical requirement for
the interconnection of the distributed resources (DR) units to the electric power system. The current
IEEE recommended industry practice is to isolate all distributed energy resources (DERs, e.g., PV and
wind) from the grid in the event of a fault in the grid. This approach is adequate when the total
capacity of the DERs is not significant and they can be removed without major impact on the system.
However it is expected that the penetration level of grid-connected DERs will increase substantially
over the next few decades. In addition, the number of Plug-in Hybrid Electric Vehicles (PHEVs) will
increase in the near future and microgrids will become popular in rural communities and commercial
buildings. The cumulative effect of these innovations will be a change in the power flow patterns in
power distribution systems.
1.1 MICROGRID AND DISTRIBUTED GENERATION
A microgrid is a cluster of loads and microsources operating as a single controllable system that
provides power to its local area. To the utility, the microgrid can be thought of as a single controllable
load that can respond in seconds to meet the needs of the transmission system. To the customer, the
microgrid can meet their special needs; such as, enhancing local reliability, reducing feeder losses,
2
supporting local voltages, providing increased efficiency through the use of waste heat, voltage sag
correction or providing uninterruptible power supply functions to name a few [2]. In ref [3], the focus
is on systems of distributed resources that can switch from grid connection to island operation without
causing problems for critical loads. Different microgrid control strategy and power management
techniques are discussed in [4-8] Premium power is a concept based on the use of power electronic
equipment (such as custom power devices and active filters), multi utility feeders and uninterruptible
power supplies to provide power to users having sensitive loads. This power must have a higher level
of reliability and power quality than normally supplied by the utility. These technologies require
power electronics to interface with the power network and its loads. In many of the cases, there is a dc
voltage source (e.g. PV), which must be converted to an ac voltage at the required frequency,
magnitude and phase angle. In these cases, the conversion will be performed using a voltage source
converter, using a possible pulse width modulation to provide fast control of voltage magnitude. The
reliability, economic operations and planning of microgrid are investigated in [9-11]. Some of the
basic issues that need to be addressed are:
• Control: A major issue in distributed generation is the technical difficulties related to control
of a significant number of microsources.
• Operation and investment: The economy of scale favors larger DG units over microsources.
For a micro source, the cost of the interconnection protection can add as much as 50% to the
cost of the system [6]. DG units with a rating of three to five times that of a microsource have
a connection cost much less per kW since the protection cost remains essentially fixed. The
microgrid concept allows for the same cost advantage of large DG units by placing many
microsources to a single dc bus with single voltage source converter interface.
• Power quality/Power Management/Reliability: DG has the potential to increase system
reliability and power quality due to the decentralization of supply. Increase in reliability
levels can be obtained if DG is allowed to operate autonomously in transient conditions [6].
1.2 POWER SHARING IN DISTRIBUTED GENERATION
Parallel converters have been controlled so as to deliver desired power (and reactive power) to the
system. Local signals are used as feedback to control converters, since in a real system, the distance
3
between the converters may make the communication impractical. A common approach for real and
reactive power sharing is droop control of two independent quantities – the frequency and the
fundamental voltage magnitude [12-22]. In this, the real power controls the system frequency, while
the reactive power controls the voltage magnitude. In [12] real and reactive power management
strategies of electronically interfaced distributed generation (DG) units in the context of a multiple-
DG microgrid system are addressed, where emphasis is primarily on electronically interfaced DG (EI-
DG) units. Robust voltage regulation with harmonic elimination under island and decoupled active
and reactive power flow control under grid-connected mode is proposed in [13]. The impact of
distributed generation technology and the penetration level on the dynamics of a test system is
investigated in [15]. The pre-planned switching events and the fault events that lead to islanding of a
microgrid are explored in [17] with the desired power sharing. The slow and oscillating nature of the
load sharing with a conventional droop control is overcome by introducing power derivative integral
terms [23], where a better controllability of the system is obtained and improvement in transient
performance is achieved. A transient droop characteristic [23] achieves a steady state invariant
frequency and good current balance. Sometimes an additional faster loop is added to program the
output impedance. Both inductive and resistive output has been investigated. In the resistive output,
the active power is controlled by terminal voltage where the reactive power is controlled by the source
angle. Karimi et al [24] developed a dynamic model and a control system for autonomous operation of
a stand-alone DG, which includes an electronically interfaced distributed resource and a local load.
The DG is represented by a DC voltage source in series with a three phase voltage-sourced converter
and an RL filter. The local load is modeled by a parallel RLC network. A state-space dynamic model is
developed for the DR (distributed resources) including the RLC network. A controller is designed to
maintain stability and control voltage and frequency of the stand-alone DG based on dynamic model
of the DG.
It is always desired in a microgrid that all the DGs respond to any load change in a similar rate to
avoid the overloading of a lagging or leading DG. In the presence of both inertial and non inertial
DGs, the response time for each DG to any change in load power demand will be different. A
converter interfaced DG can control its output voltage instantaneously and so the change in the power
demand can be picked up quickly, while in an inertial DG, the rate of change in power output is
4
limited by the machine inertia. To ensure that a load change is picked up by all the DGs in same rate,
the rate of change in converter interfaced DGs is to be limited.
1.2.1 CONTROLS FOR GRID AND ISLAND OPERATION
Power electronic interfaces introduce new control issues and possibilities. It is necessary to create
a power electronic interface, which allows large clusters of micro generators to operate in both an
island mode and as a satellite to the power grid while providing a high quality of power at a minimum
equipment cost. Basic requirements of the power electronic interface are:
• To provide fixed power and local voltage regulation
• To facilitate DG fast load tracking using storage
• To incorporate “frequency droop” methods to insure load sharing between micro-sources in
islanded operation without communications
Keyhani et all [25] propose the use of a low-bandwidth data communication system along with
locally measurable feedback signal for each DG. This is achieved by combining two control methods:
droop control method and average power control. The average power method with a slow update rate
is used in order to overcome sensitivity voltage and current measurement errors. In addition, a
harmonic droop scheme for sharing harmonic content of the load currents is also proposed. But the
communication between DGs may not be always possible in reality due to the physical distance
between them. The application of adaptive control or robust control in distributed generation is shown
in [26-27]. A strategic analysis and optimal voltage control technique for distributed generation are
proposed in [28 and 29].
1.3 POWER QUALITY AND RELIABILITY
A microgrid may contain non linear unbalanced loads. Moreover the voltage source converter
(VSC) connecting the DGs are themselves sources of harmonic generation. Therefore, it is important
to ensure a compensator configuration that is suitable for supplying electrical power to the microgrid,
while at the same time compensating for the non linearity/unbalance.
5
Power quality is always been a major concern and different filtering techniques are proposed in [30,
31, 32]. Determination of allowable penetration levels of distributed generation resources based on
harmonic limit consideration has been addressed in [33]. Many optimization methods are also been
proposed for planning and energy loss reduction [34, 35 and 36].
The authors of [37] propose a single-phase high-frequency ac (HFAC) microgrid as a solution
towards integrating renewable energy sources in a distributed generation system. For a better
performance of the DGs and more efficient power management system, it is important to achieve
control over the power flow between the grid and the microgrid. With a bidirectional control on the
power flow, it is possible not only to specify the exact amount of power supplied by the utility but
also the fed back power from microgrid to utility during lesser power demand in the microgrid.
Reliability is also a major issue in microgrid operation. Frequent load change, DG location and
change in DG power output always challenge the power management system and system reliability.
From the reliability point of view, frequency isolation between a microgrid and utility may be
desirable.
With number of DGs and loads connected over a wide span of the microgrid, isolation between the
grid and the microgrid will ensure a safe operation, in most cases.. Any voltage or frequency
fluctuation in the utility side has direct impact on the load voltage and power oscillation in the
microgrid side. For a safe operation of any sensitive load, it is not desirable to have any sudden
change in the system voltage and frequency. The isolation between the grid and microgrid not only
ensures safe operation of the microgrid load, it also prevents direct impact of microgrid load change or
change in DG output voltage on the utility side.
Protection of the devices both in utility and microgrid sides during any fault is always a major
concern [38-42]. Of the many schemes that have been proposed, [38] explores the effect of high DG
penetration on protective device coordination and suggests an adaptive protection scheme as a
solution to the problems. In [39], a method has been proposed for determining the coordination of the
rate of change of frequency (ROCOF) and under/over-frequency relays for distributed generation
protection considering islanding detection and frequency-tripping requirements. The method is based
on the concept of application region, which defines a region in the trigger time versus active power
imbalance space where frequency-based relays can be adjusted to satisfy the anti-islanding and
frequency-tripping requirements simultaneously.
6
1.4 SYSTEM STABILITY
The system stability during load sharing has been explored by many researchers [13, 15, and 43].
The Transient stability of the power system with high penetration level of power electronics interfaced
(converter connected) distributed generation is explored in [13]. But the study is based on presence of
an infinite bus. The other important issue, with isolated operation of the power system network has
been overlooked in the study. A scheme for controlling parallel connected converter in a standalone ac
system is presented in [44]. A modular structure of the controller is presented. The structure can be
modified to meet the control requirement for any other ac system. The scheme proposed a P-I
regulator to determine the set points for generator angle and flux. The dynamic performance of the
system can be substantially improved by using other advanced control technique. Similar to the small-
signal stability of conventional power system, [45] establishes how the control scheme gives rise to
the oscillatory modes with poor damping. To identify the possible feedback signals for controllers, a
sensitivity analysis is carried out. The low frequency stability problem with change in power demand
is investigated in [46]. It is shown that with the change in power demand, the movement of the low
frequency oscillations to new location affects the relative stability of the system. The decentralized
control strategies for parallel converters are shown in [47 and 48].
The robust stability of a voltage and current control solution for a stand-alone distributed generation
(DG) unit is analyzed in [49] using structured singular values. This results in a discrete-time sliding
mode current controller. In [50], small-signal stability analysis of the combined droop and average
power method for load sharing control of multiple distributed generation systems in a stand-alone ac
supply mode is discussed. A small-signal model is developed and its accuracy is verified from
simulations of the original nonlinear model.
Modeling and analysis of autonomous operation of converter-based microgrid is presented in [20,
51], in which the converters are controlled based on voltage and frequency droop. Each sub-module of
the system is modeled in state-space form and all the modules are then combined together on a
common reference frame. The model captures the detail of the control loops of the converter but not
the switching action. Normal PI controllers are used for voltage and current control.
7
1.5 POWER SHARING IN RURAL NETWORK
Rural electrification should ensure the availability of electricity irrespective of the technologies,
sources and forms of generation, but many cannot afford it due to a shortage of resources. Distributed
generation is one of the best available solutions for rural microgrids. However the locations of the
micro sources are very important. The success or failure of the rural electrification activities in a
developing country invariably depends on the extent to which the relevant issues have been
systematically analyzed and addressed. Power electronic converter solution is introduced that is
capable of providing rural electrification at a fraction of the current electrification cost. For weaker
networks, this inevitably leads to poor voltage regulation.
A highly resistive line, typical of low or medium voltage rural networks, challenges the power
sharing controller efficacy. The strong coupling of real and reactive power in the network leads to an
inaccurate load frequency control. High values of droop gains are required to ensure proper load
sharing, especially under weak system conditions. However, high droop gains have a negative impact
on the overall stability of the system. Moreover, proper load sharing cannot be ensured even with a
high gain if the lines are highly resistive. In such cases, the main assumption of the droop control that
active and reactive powers are decoupled is violated and the conventional droop control [43] is not
able to provide an acceptable power sharing among the DGs.
The decoupling of the real and reactive power is achieved in [52] for a high R/X line with
frequency droop control. It is shown that a modification of the droop equation can accommodate the
effect of line impedance. However, the choice of droop gains for rating based sharing of power has
not been addressed in [52].
As discussed previously, in the case of voltage source converter (VSC) based DGs, the output
angle can be changed instantaneously and so drooping the angle is a better way to share load [53].
Frequency regulation constraint limits the allowable range of frequency droop gain, which in turn,
may lead to chattering during frequent load changes in a microgrid. In [54], it is assumed the lines are
mainly resistive and conventional droop can work with real power controlled by voltage and reactive
8
power by angle. But in a rural network a high R/X ratio is common. With a strong coupling of real
and reactive power, they cannot be controlled independently with either frequency or voltage and so
the droop equations need to be modified. The real power droop coefficients can be chosen depending
on the load sharing ratio.
It is often difficult to install extensive distribution network, especially since the customer density in
the rural areas can be sparse. Distributed generation is one of the best available solutions for such a
predicament. Planning of a typical medium-voltage rural distribution system in different loading
conditions is discussed in [55-57]. The bottom up approach through an evaluation of autonomous or
non-autonomous modified microgrid concept to provide electricity to local residents is proposed in
[56].
The policy and prospective planning achievements for rural electrification are hindered in many
countries are described in [58-69]. Electrification in Africa, Uganda, Nepal or India has their own site
specific requirements [63, 65, 66 and 68]. The general rural electrification is described in [61].
Planned islanding in rural distribution system is demonstrated in [69].
The off grid renewable connection at Anangu Solar Station of South Australia [70], where 220 kW
power is distributed covering 10,000 square km among number of communities up to 500 people or
minigrid connection at Hermannsburg in central Australia [70], where three communities each with
several hundred households with 720 kW total power consumption are the examples of the scenario
where the converter interfaced micro sources and loads are geographically far from each other in a
low voltage network.
1.6 OBJECTIVES OF THE THESIS AND SPECIFIC CONTRIBUTIONS
The objectives of the thesis and the specific contributions are discussed in this section.
1.6.1 OBJECTIVES OF THE THESIS
Based on gaps in the literature, the objectives of the research are set as,
• To improve power sharing techniques in a microgrid with converter interfaced sources.
9
• To facilitate load frequency control of the microgrid and a smooth transition between grid
connected and islanded mode.
• To enhance power quality in a microgrid which may contain unbalanced and non linear loads.
• To improve power management system and reliability of the microgrid:
• To perform stability analysis and enhancement in stability with supplementary controller
• To achieve superior power sharing in rural network with high R/X lines.
1.6.2 SPECIFIC CONTRIBUTIONS OF THE THESIS
Based on the above objectives, the specific contributions of this thesis are
1. An angle droop controller is proposed to share power amongst converter interfaced DGs in a
microgrid. As the angle of output voltage can be changed instantaneously in a voltage source
converter (VSC), controlling the angle to control the real power is beneficial for quick
attainment of steady state. Thus converter based DGs, load sharing can be done by drooping
the converter output voltage magnitude and its angle instead of system frequency. The angle
control results in much lesser frequency variation compared to the frequency variation with
frequency droop.
2. An enhanced frequency droop controller is proposed for better dynamic response and smooth
transition between grid connected and islanded mode of operation. A modular controller
structure with modified control loop is proposed for better load sharing between the parallel
connected converters in a distributed generation system. The integral control in the voltage
angle loop helps to influence the close loop dynamics without affecting the steady state
frequency regulation. Moreover, a smooth transition between grid connected mode and
islanded mode is very important to ensure a superior system performance.
3. Power quality enhanced operation of a microgrid with unbalanced and non linear loads is
addressed. The proposed controllers are capable of compensating the local unbalanced and
non linear loads. The local loads can be shared with utility in any desired ratio. The common
loads which are normally supplied by the utility in grid connected mode, shared among the
DGs proportional to their rating in the islanded mode.
4. An isolation technique between microgrid and utility, for better reliability, is proposed by
using a back-to-back converter. As utility and microgrid are totally isolated, the voltage or
10
frequency fluctuations in the utility side do not affect the microgrid loads. Proper switching
of the breaker and other power electronics switches has been proposed during islanding and
resynchronization process. With a bidirectional power flow, it is possible to control the
power flow to and from the utility and microgrid.
5. A linearized state space model of an autonomous microgrid supplied by all converter based
DGs and connected to number of passive loads is formed. The proposed generalized model is
valid even when the network is complex containing any number of DGs and loads. The
model is utilized for eigenvalue analysis around a nominal operating point. A supplementary
loop is proposed around the primary droop control loop of each DG converter to stabilize the
system despite having high gains that are required for better load sharing. The control loops
are based on local power measurement that modulates of the d-axis voltage reference of each
converter. The coordinated design of supplementary control loops for each DG is formulated
as a parameter optimization problem and is solved using an evolutionary technique.
6. Two methods are proposed for load sharing in an autonomous microgrid in rural network
with high R/X ratio lines. The first method proposes power sharing without any
communication between the DGs. The feedback quantities and the gain matrices are
transformed with a transformation matrix based on the line resistance-reactance ratio. The
second method is with minimal communication based output feedback controller. The
converter output voltage angle reference is modified based on the active and reactive power
flow in the line connected at PCC. It is shown that a more economical and proper power
sharing solution is possible with the web based communication of the power flow quantities.
Publications covering the contribution of this thesis are given in Appendix B.
1.7 THESIS ORGANIZATION
The thesis has been organized in seven chapters. This chapter presents the relevant literature
survey and sets the motivation for the research work carried out in this thesis.
11
Chapter 2 compares the performance of angle and frequency droops in an autonomous microgrid
that only contains voltage source converter (VSC) interfaced distributed generators. As a VSC can
instantaneously change output voltage waveform, power sharing in a microgrid is possible by
controlling the output voltage angle of the DGs through droop. The angle droop is able to provide
proper load sharing among the DGs without a significant steady state frequency drop in the system. It
is shown that the frequency variation with the frequency droop controller is significantly higher than
that with the angle droop controller.
In Chapter 3, the control methods for proper load sharing between parallel converters connected
to microgrid supplied by distributed generators is described. A control strategy is proposed to improve
the system performance through seamless transfer between islanded and grid connected modes. The
smooth transition between the grid connected and off grid mode is achieved by changing the control
mode from voltage control in islanded mode to state feedback control in grid connected mode. Its
efficacy has been validated through simulation for various operating conditions.
A control strategy is proposed in Chapter 4 to improve power quality and proper load sharing in
both islanded and grid connected modes. It is assumed that each of the DGs has a local load connected
to it, which can be unbalanced and/or nonlinear. The DGs compensate the effects of imbalance and
nonlinearity of the local loads. Common loads are also connected to the microgrid, which are supplied
by the utility grid under normal conditions. However during islanding, each of the DGs supplies its
local load and shares the common load through droop characteristics.
Chapter 5 proposes a method for power flow control between utility and microgrid through
back-to-back converters, which facilitates isolation and desired controlled real and reactive power
flow between utility and microgrid. In the proposed control strategy, the system can run in two
different modes depending on the power requirement in the microgrid. In mode-1, specified amounts
of real and reactive power are shared between the utility and microgrid through the back-to-back
converters. Mode-2 is invoked when the power that can be supplied by the DGs in the microgrid
reaches its maximum limit. In such a case, the rest of the power demand of the microgrid has to be
supplied by the utility.
The problem of appropriate load sharing in an autonomous microgrid is investigated in chapter 6.
High gain angle droop control ensures proper load sharing, especially under weak system conditions.
However it has a negative impact on the overall stability. Frequency domain modeling, eigenvalue
12
analysis and time domain simulations are used to demonstrate this conflict. A supplementary loop is
proposed around the conventional droop control of each DG converter to stabilize the system while
using high angle droop gains. The control loops are based on local power measurement that
modulation of the d-axis voltage reference of each converter.
Chapter 7 proposes new droop control methods for load sharing in a rural area with distributed
generation. To overcome the conflict between higher feedback gain for better power sharing and
system stability in angle droop, two control methods have been proposed. The first method considers
no communication among the distributed generators (DGs) and regulates the converter output voltage
and angle ensuring proper sharing of load in a system having strong coupling between real and
reactive power due to high line resistance. The second method, based on a smattering of
communication, modifies the reference output voltage angle of the DGs depending on the active and
reactive power flow in the lines connected to point of common coupling (PCC).
The general conclusions and scope for future works are given in Chapter 8. Appendix A
discussed the converter structure and control methods used in the thesis.
13
CHAPTER 2
POWER SHARING WITH CONVERTER INTERFACED SOURCES
With the growth of distributed generation and its operation in tandem with utility power supply,
the interconnection of distributed generators (DGs) to the utility grid through power electronic
converters has raised concern about system control and power sharing among the DGs. Control of the
DG system is important and system regulation such as frequency deviation and voltage drop becomes
very crucial during the decentralized power sharing through droop control.
This chapter presents, the power sharing in microgrid with converter interfaced sources. The
conventional frequency droop control is first demonstrated. As the sources are converter interfaced, it
is possible to control the output voltage angles instantaneously. The proposed angle droop control is
derived from load flow analysis and demonstrated in a similar system to compare the performance of
both the droop controllers.
2.1 CONTROL OF PARALLEL CONVERTERS FOR LOAD SHARING WITH
FREQUENCY DROOP
The basic power system model with two DG sources connected to the load at the point of common
coupling (PCC) is shown in Fig. 2.1. The load can be a constant impedance load or a motor load. The
converter output voltages are denoted by V1∠δ1 and V2∠δ2 and are connected to the microgrid with
output filter of inductance L1.and L2. . P1, P2 and Q1, Q2 represent the real and reactive power supplied
by the DGs while PL and QL are respectively the real and reactive power demand of the load. The line
resistances are denoted by R1 and R2 while Lline1 and Lline2 represent the line inductances.
14
Fig. 2.1. Microgrid system under consideration.
2.1.1 FREQUENCY CONTROL
The conventional droop control method is given by [43]
nQVV
mPs
−=
−=∗
ωω (2.1)
where m and n are the droop coefficients, ωs is the synchronous frequency, V is the magnitude of the
converter output voltage and ω is its frequency, while P and Q respectively denote the active and
reactive power supplied by the converter. Thus the frequency and the voltage are being controlled by
the active and reactive power output of the DG sources.
2.1.2 MODULAR CONTROL STRUCTURE
A modification to the conventional droop controller is proposed here. This is shown in Fig. 2.2
for DG-1 only. A similar structure is also used for DG-2. The output voltage V1∠δ1 and output current
I1 of the converter are used for calculating the real power (P1) and reactive power (Q1) injected by
DG-1. These are then used in (2.1) to calculate ωs and V1*. The quantity ωs and the angle of the PCC
voltage δPCC are then used to calculate the reference angle δ1*. This is described in Section 2.1.3. The
reference magnitude V1* and its angle δ1
* are then used to generate the instantaneous reference
voltages of the three phases which are then compared with the measured instantaneous phase voltages
of V1. The resultant error is used in the feedback control to generate the firing pulses (u) of VSC-1.
The feedback control and converter structure are discussed in Appendix-A. In islanded mode state
feedback control (A.4) is used while voltage control (A.3) is employed in the grid connected
operation.
15
Fig. 2.2. The modular control structure
2.1.3 CONVERTER VOLTAGE ANGLE CALCULATION
The converter voltage angle control loop is shown in Fig. 2.3. The frequency ω1 is calculated from
the droop given in (2.1) and is then compared with the frequency (ωPCC) of the PCC voltage. The error
is passed through an integrator with a gain of KI and is then added with the integral of ωPCC to obtain
φ1*. The angle φ1
* rotates at the synchronous speed ωs making an angle δ1* with the reference.
Changing the value of KI, we can influence the close loop dynamics without affecting the steady state
frequency regulation.
Fig. 2.3. Voltage angle control loop.
2.1.4 REFERENCE GENERATION
With respect to Fig. A.3 in Appendix A, a state vector is defined as
[ ]1iivx cfcfT = (2.2)
The reference for vcf is v1*, as mentioned in the previous sub-section. Given V1
* and φ1*, the phasor
current through the capacitor Cf is given by
16
( )°+∠= ∗∗∗ 9011 δω VCI fcf (2.3)
The reference icf* is obtained from the instantaneous value of Icf
*.
The reference for i1 is derived through its phasor quantity I1*. Fig. 2.1 identifies that if the
references are strictly followed
*1
*1
*111 )( IVjQP ×−∠=− δ (2.4)
It is to be noted that in this section * denote reference quantities and not conjugate functions.
Let us define I1* = I1p
* + j I1q*. Then from 2.4,
[ ][ ]∗∗
∗∗
∗∗∗
∗
−=
+=
11111
1
11111
1
cossin1
sincos1
δδ
δδ
QPV
I
QPV
I
q
p
(2.5)
Therefore the phasor reference is given by
+= ∗
∗−∗∗∗
p
qqp
I
IIII
1
11111 tan (2.6)
The voltage angle controller of Fig. 2.3 generates a rotating angle φ1*, which is equal to ωst + δ1
*.
The angle φ1* is reset after every 2π. Fig. 2.6 shows the variation along with the reference ωst. From
this figure, we can write
∗+== 110 2 δωπω tt ss
Therefore
( )011 tts −=∗ ωδ (2.7)
Fig. 2.6. Source angle extraction from rotating angle.
17
Once the references for the state vector are obtained, the control law is computed as shown in
Appendix-A with the state feedback controller (A.4).
2.2 ANGLE DROOP CONTROL
The DGs have the potential to deliver reliable power when their locations are strategically planned.
However, for large scale application of DGs, the commercial and regulatory challenges have to be
considered before their benefits can be realized [71]. One of the most significant aspects is the change
in system frequency. As discussed in [12-14], DG real power output is controlled by dropping the
system frequency. Depending on the stiffness of the power-frequency curve, the steady state
frequency will change with the changes in system loads.
It is not desirable to operate the system in a much lower frequency and a complimentary frequency
restoration strategy is proposed in [43]. The reference powers of the DGs are modified to restore the
frequency which is equivalent to shifting the power-frequency curve vertically. The process can be
controlled in a slow, coordinated manner by a master controller, using a slow communication channel
between the converters [43]. In conversational frequency droop, the frequency deviation signal is used
to set the power output of the converter. The limitations of the use of frequency deviation alone have
been established for many years [72]. Nevertheless, the conventional droop method has several
drawbacks that limit its application, such as: slow transient response, frequency and amplitude
deviations, imbalanced harmonic current sharing, and high dependency on converter output-
impedance [73]. High frequency signals are injected to overcome the imbalance reactive power flow.
Since the power balance and the system stability rely on these signals, the application of such signal
increases system complexity and reduces reliability.
It is possible for a VSC to instantaneously change its output voltage waveform and power sharing
in a microgrid by controlling the output voltage angle of the DGs through droop. Let us consider same
microgrid system as shown in Fig. 2.1 is considered. First, the load sharing with angle droop is
derived using the DC load flow method. It is possible to share power among the DGs proportional to
their rating by dropping the output voltage angles.
The angle droop control strategy is applied to all the DGs in the system. It is assumed that the total
power demand in the microgrid can be supplied by the DGs such that no load shedding is required.
18
The output voltages of the converters are controlled to share the load proportional to the rating of the
DGs. As an output inductance is connected to each of the VSCs, the real and reactive power injection
from the DG source to the microgrid can be controlled by changing voltage magnitude and its angle
[12-14]. Fig. 2.7 shows the power flow from a DG to the microgrid where the RMS values of the
voltages and current are shown and the output impedance is denoted by jXf. It is to be noted that real
and reactive power (P and Q) shown in the figure are average values.
Fig. 2.7. DG connection to microgrid.
2.2.1. ANGLE DROOP CONTROL AND POWER SHARING
The average real power is denoted by P and the reactive power by Q. These powers, from the DG to
the microgrid, can then be calculated as
( )
( )f
tt
f
tt
X
VVVQ
XVV
P
δδ
δδ
−×−=
−×=
cos
sin
2 (2.8)
These instantaneous powers are passed through a low pass filter to obtain the average real and
reactive power P and Q. It is to be noted that the VSC does not have any direct control over the
microgrid voltage at the bus Vt∠δt (see Fig. 2.7). Therefore from (2.8), it is obvious that if the angle
difference ( − t) is small, real power can be controlled by controlling , while the reactive power can
be controlled by controlling voltage magnitude. Thus the power requirement can be distributed among
the DGs, similar to a conventional droop by dropping the voltage magnitude and angle as
( )( )ratedrated
ratedrated
QQnVV
PPm
−×−=−×−= δδ
(2.9)
19
where Vrated and rated are the rated voltage magnitude and angle respectively of the DG, when it is
supplying the load to its rated power levels of Prated and Qrated. The coefficients m and n respectively
indicate the voltage angle drop vis-à-vis the real power output and the voltage magnitude drop vis-à-
vis the reactive power output. These values are chosen to meet the voltage regulation requirement in
the microgrid.
To derive power sharing with angle droop, a simple system of Fig. 2.1 with two machines and a
load is considered. Applying DC load flow with all the necessary assumptions we get,
2222
1111
)(
)(
PXX
PXX
L
L
+=−
+=−
δδδδ
(2.10)
where X1 = L1/(V1V) , XL1 = LLine1/(V1V), X2 = L2/(V2V) and XL2 = LLine2/(V2V).
From (2.9), the angle droop equations of the two DGs are given by
( )( )ratedrated
ratedrated
PPm
PPm
22222
11111
−×−=−×−=
δδδδ
(2.11)
The offsets in the angle droop are such that when DG output power is zero, the DG source angle is
zero. Therefore the rated droop angles are taken as 1rated = m1P1rated and 2rated = m2P2rated. Then from
(2.11) we get
221121 PmPm −=−δδ (2.12)
Similarly from (2.10) we get
22211121 )()( PXXPXX LL +−+=−δδ (2.13)
Assuming the system to be lossless (as normally used in DC load flow), we get,
LLL
L
LLLL
PmXXmXX
mXXP
PPmPmPPXXPXX
111222
2221
1211122111 )())(()(
+++++++=
−−=−+−+ (2.14)
Similarly P2 can be calculated as
LLL
L PmXXmXX
mXXP
111222
1112 +++++
++= (2.15)
From (2.14) and (2.15), the ratio of the output power is calculated as,
20
111
222
2
1
mXXmXX
PP
L
L
++++= (2.16)
It is to be noted that the value of X1 and X2 are very small compared to the value of m1 and m2.
Moreover if the microgrid line is considered to be mainly resistive with low line inductance and the
DG output inductance is much larger, we can write
222111 and LL XXmXXm >>>>>>>>
Therefore from (2.16), it is evident that the droop coefficients play the dominant role in the power
sharing. Since the droop coefficients are taken as inversely proportional to the DG rating, from (2.16)
we can write
rated
rated
PP
mm
PP
2
1
1
2
2
1 =≈ (2.17)
The above approximation can incorporate little error in power sharing ratios depending on the
droop gain and inductances values. The error is further reduced by taking the output inductance (L1
and L2) of the DGs inversely proportional to power rating of the DGs. If the microgrid line is
inductive in nature and of high value, then knowledge about the network is needed.
2.3 ANGLE DROOP AND FREQUENCY DROOP CONTROLLER
The converter structure is given in Appendix A (A.1). Both the angle and frequency droop
controllers are modeled separately from their droop equations (2.9) and (2.1) respectively. The droop
controller model is then combined with the converter model. All the combined converter and
controller models are converted to a common reference frame and then connected to the network to
derive the entire microgrid model as shown in [51]. The microgrid model is used to select the
parameters of the droop controllers through eigenvalue analysis. The detail converter model with
droop equation is given in Chapter 6.
The droop controllers are designed based on the composite model discussed above. The system
parameters considered for the study are given in Table-2.1. The eigenvalue trajectory is plotted by
varying either the angle droop or frequency droop gain. The voltage droop gain is held constant. Fig.
2.8 shows one of the dominant complex conjugate eigenvalue trajectories with the angle droop
21
controller. It can be seen that, the complex pole crosses the imaginary axis, for a droop controller gain
of 0.00045 rad/kW. Similarly Fig. 2.9 shows the corresponding eigenvalue trajectory as function of
frequency droop controller gain.
Fig.2.8. System stability as function of frequency droop gain.
Fig. 2.9. System stability as function of angle droop gain.
To compare the results of the two droop controllers, the nominal values of the controller gain are
chosen at 75% of the gain at which the system becomes unstable. This implies that the gain with the
angle droop controller is m = 0.00034 rad/kW and with the frequency droop controller is mω =
0.000375 rad/s/kW.
22
TABLE-2.1: SYSTEM AND CONTROLLER PARAMETERS
System Quantities Values
Systems frequency 50 Hz
Load ratings
Load
2.8 kW to 3.1 kW
DG ratings (nominal)
DG-1
DG-2
1.0kW
1.33kW
Output inductances
LG1
LG2
75 mH
56.4 mH
DGs and VSCs
DC voltages (Vdc1 to Vdc4)
Transformer rating
VSC losses (Rf)
Filter capacitance (Cf)
Hysteresis constant (h)
0.5kV
0.415kV/0.415 kV, 0.25 MVA, 2.5% Lf
0.1 Ω
50 µF
10-5
Angle Droop Controller
m1 0.000340 rad/kW
m2 0.000255 rad/kW
Frequency Droop Controller
mw1 0.000375 rad/s/kW
mw2 0.000281rad/s/kW
2.4 SIMULATION STUDIES
Simulation studies are conducted with different types of load and operating conditions to check the
system response and controller action. Some of the results are discussed below. The system data used
is given in Table 2.1.
2.4.1 FREQUENCY DROOP CONTROLLER
The frequency droop controller is employed to share power in this case. The output impedances of
the two sources are chosen in a ratio of DG-1: DG-2 = 1:1.33 and the power rating of these DGs are
also chosen in the ratio of 1.33:1. To investigate the power sharing in a constant load changing
situation, the load conductance is chosen as the integral of a Gaussian white noise with zero mean and
a standard deviation of 0.01 Mho. The system parameters and the controller gains are shown in Table-
2.1.The power outputs of the DGs are shown in Fig. 2.10.
23
Fig. 2.10. DG power output with frequency droop control.
2.4.2 ANGLE DROOP CONTROLLER
The same system is used to investigate the angle droop controllers. Fig. 2.11 shows the power
output of the DGs in case of the angle droop controller. It can be seen that the constant deviation in
power output from the DGs are always in the desired ratio and the fluctuation in output power is
almost 10% as per the load change.
Fig. 2.11. DG power output with angle droop control.
24
2.4.3 COMPARISON OF FREQUENCY DROOP AND ANGLE DROOP
To compare the performance of the controllers, the frequency deviation is presented for
both cases. The frequency deviation of the DG sources is shown in Fig. 2.12. It is evident that the
frequency variation with the frequency droop controller is significantly high.
The standard deviation with the frequency droop controller is 0.4081 rad/s and 0.4082 rad/s for the
two DGs. It can also be seen that the mean frequency deviation is large.
Fig. 2.12. Frequency variation with frequency droop control
Fig. 2.13 shows the frequency deviation with the angle droop control. The steady state frequency
deviation is zero-mean and the standard deviation of the frequency deviation is 0.01695 rad/s and
0.01705 rad/s respectively for DG-1 and DG-2. The deviation in the frequency is small and the angle
droop controller is able to share load in the desired ratio despite the random change in the load
demand. This demonstrates that the angle droop controller generates a substantially smaller frequency
variation than the conventional frequency droop controller. Fig. 2.14 shows the angle deviation with
the angle droop. It can be seen that the nature of angle deviation is similar to the frequency deviation
with the frequency droop.
25
Fig. 2.13. Frequency variation with angle droop control.
Fig. 2.14. Angle variation with angle droop control.
2.4.4 ANGLE DROOP IN MULTI DG SYSTEM
To investigate the efficacy of the angle droop controller in a microgrid with multiple DGs and
loads, angle droop controllers are designed for the system shown in Fig. 2.15 with system parameter
shown in Table-2.2. It has four DGs and five loads as shown. It is desired that DG-1 to DG-4 share the
load in 1.0:2.0:1.5:1.5 ratio (to share power proportional to the DG rating). With the system running at
steady state, the loads Ld2 and Ld3 are disconnected at 0.2 s. The power sharing among the DGs is
shown in Fig. 2.16.
26
Fig. 2.15. Microgrid Structure with multiple DGs.
TABLE-2.2: MICROGRID SYSTEM AND CONTROLLER PARAMETERS
System Quantities Values
Systems frequency 50 Hz
Feeder impedance
Z12 = Z23 = Z34 = Z45 = Z45 = Z56 =
Z67 = Z78 = Z89
0.1 + j 0.6 Ω
Load ratings
Ld1
Ld2
Ld3
Ld4
Ld5
1.8 kW and 1.6 kVAr
0.8kW and 0.6 kVAr
0.8 kW and 0.6 kVAr
0.8 kW and 0.6 kVAr
1.8 kW and 1.6 kVAr
DG ratings (nominal)
DG-1
DG-2
DG-3
DG-4
1.0kW
2.0kW
1.5 kW
1.5 kW
Output inductances
LG1
LG2
LG3
LG4
75 Mh
37.5 mH
50 mH
50mH
DGs and VSCs
DC voltages (Vdc1 to Vdc4)
Transformer rating
VSC losses (Rf)
Filter capacitance (Cf)
Hysteresis constant (h)
0.5kV
0.415kV/0.415 kV, 0.25 MVA,
2.5% Lf
0.1 Ω
50 µF
10-5
Angle Droop Controller
in multi machine
m1 0.1 rad/MW
m2 0.05 rad/MW
m3 0.075 rad/MW
m4 0.075 rad/MW
The efficacy of the angle droop is further verified by sharing power only between DG-1 and DG-4,
when DG-2 and DG-3 are disconnected from the system. Let us assume that the system is running in
the steady state supplying the loads Ld1, Ld2 and Ld4. At 0.2 s, the load Ld4 is disconnected. The
27
system response is shown in Fig. 2.17. This test studies the controller response when the power
generation and load demand is not evenly distributed along the microgrid. It can be seen that after 0.2
s, the sharing is not very accurate. Choosing a higher droop controller gain, we can assure better
sharing in such situations. However, a very high value of droop gain can lead the system to instability
as shown in eigenvalue trajectory of Fig. 2.9. The choice of controller gain is thus a trade off between
system stability and system response.
Fig. 2.16. Real Power Sharing of the DGs.
Fig.2.17. Real Power Sharing of the DG-1 and DG-4.
2.5 CONCLUSIONS
A modular controller structure with modified voltage angle control loop is proposed for better load
sharing between the parallel connected converters in a distributed generation system. The integral
28
control in the voltage angle loop helps to influence the close loop dynamics without effecting the
steady state frequency regulation. The efficacy of angle droop over frequency droop in a voltage
source converter based autonomous microgrid is also demonstrated in this chapter. The power sharing
of the DG sources with angle droop is derived first. A frequency droop controller and an angle droop
controller are designed to ensure the same stability margin in a two DG system. It is shown that the
frequency variation with the frequency droop controller is significantly higher than that with the angle
droop controller. The efficacy of the angle droop controller is further verified in a microgrid with
moderate number of DGs and loads. It is to be noted that, angle droop requires measurement of angle
with respect to a common reference frame and GPS phasor measurement can be used for this purpose.
Frequency droop does not require any GPS measurement. Moreover, with the presence of inertial DGs
(synchronous machine), it is easier to share power with the frequency droop controller. In the next
chapter, the frequency droop controller is discussed for a smooth transfer between grid connected and
islanded operations.
29
CHAPTER 3
LOAD FREQUENCY CONTROL IN MICROGRID
A smooth transfer between the grid connected and standalone modes is essential for a reliable
operation in a microgrid. Control of the DG system is important in both the grid connected and
islanded mode and system stability becomes very crucial during the transfer between grid connected
and islanded mode. A seamless transfer can ensure a smooth operation with proper load sharing and
quick attainment of steady state.
In this chapter a scheme for controlling parallel connected converters in islanded and grid
connected mode are presented. The control techniques for a smooth transfer between these two modes
are also shown. A modular structure of the controller is used as described in Chapter 2. Later the
frequency droop controller strategy is applied to a microgrid containing both inertial and inertia-less
DGs. To investigate the operation of all the micro-sources together, a microgrid is planned at
Queensland University of Technology (QUT) where the main issue is decentralized power sharing and
system stability. As mentioned in Chapter 2, a converter interfaced DG can control its output voltage
instantaneously and so the change in the power demand can be picked up quickly, while in an inertial
DG, the rate of change in power output is limited by the machine inertia. To ensure that a load change
is picked up by all the DGs at the same rate, the rate of change in converter interfaced DGs needs to
be limited. To investigate the system response with the dynamics of the DG units, the sources and all
the power electronic interfaces are modeled in detail.
3.1 SEAMLESS TRANSFER BETWEEN GRID CONNECTED AND ISLANDED
MODES
The basic power system model with two DG sources connected to the load at the point of common
coupling (PCC) is shown in Fig. 3.1. In this, the system runs in islanded mode when the circuit
breaker (CB) is open; otherwise it runs in grid connected mode. The load can be a constant impedance
30
load or a motor load. In Fig. 3.1, the voltage source VS is the utility voltage that is connected to the
PCC with a feeder of impedance RS + jXS. The current drawn from the utility is denoted by Ig, while Pg
and Qg are respectively the real and reactive power supplied by the grid. It is assumed that the DGs are
constant dc voltage sources Vdc1 and Vdc2. The converter output voltages are denoted by V1∠δ1 and
V2∠δ2 and they are connected to the PCC through reactances jX1 and jX2 respectively. P1, P2 and Q1,
Q2 represent the real and reactive power supplied by the DGs.
Fig. 3.1. Microgrid system under consideration.
3.1.1 PROPOSED CONTROL
The frequency droop controller described in Chapter 2 has been employed here. The detail
converter structure is also the same as given in Appendix A (A.1).
1. As discussed in the last chapter the voltage regulation is a problem with frequency droop when
the load changes frequently. In this chapter it is shown that better load sharing and a rapid steady
state attainment are achieved when the voltage control is used in the islanded mode, while the
state feedback ensures better response in the grid connected mode (Detail converter control
techniques are discussed in Appendix A). A seamless transfer between these two modes is
proposed by changing state feedback to voltage control and vice versa. Ordinarily, in the grid
connected mode, the DGs operate under the state feedback control. When an islanding is
detected, the DGs are switched to the voltage control mode. These are switched back to the state
feedback control mode after resynchronization.
31
3.1.2 SIMULATION STUDIES
Simulation studies are carried out with different type loads and operating conditions to check the
system response and controller action. Some of the results are discussed below. The system data used
are given in Table 3.1.
3.1.2.1 ISLANDED MODE
In the islanded mode, the VSCs are operated in voltage control mode through output feedback. In
this mode, the grid is not available and the total power demand of the load is supplied by the DGs.
The frequency is also not fixed and is calculated from the modified droop to meet the active and
reactive power requirements. With any load change, the active and reactive power requirements
change and the VSC reference voltage magnitude and angle must change to meet the new load
requirement. Two types of load are considered here – constant impedance type load and motor load.
Fig. 3.2 shows the response with impedance load, where the values of the load impedances are
doubled at 1 s. The load is changed back to its nominal value at 1.5 s. It can be seen that DG-1 shares
more load than DG-2 in accordance with their droop characteristics, while the grid does not supply
any power.
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7-0.5
0
0.5
1
1.5
Act
ive
pow
er (M
W)
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7-0.2
00.20.40.6
Rea
ctiv
e p
ower
(M
VAR
)
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7-0.1
0
0.1
Time(s)
Cu
rren
t-ph
ase
a (k
A)
DG1DG2Grid
DG1DG2Grid
DG1DG2Grid
Fig.3.2 System response with impedance load in islanded mode.
Fig. 3.3 shows the results when the inductor motor is connected in parallel with the passive load at
2 s and disconnected at 2.75 s. The motor is operated in speed control mode. The change in active
32
power supplied by the DGs and output current of the converters show proper load sharing with a quick
steady state attainment. The zero power and zero current from the grid confirm the islanded condition.
TABLE 3.1. SYSTEM PARAMETERS
System Quantities Values
Systems Frequency (ωs) 100π rad/s
Source voltage (Vs) 11 kV rms (L-L)
Feeder impedance (Rs + jXs) 3.025 + j12.095
DG-1
DC voltage (Vdc1)
Transformer rating
VSC losses
Source inductance (L1)
Filter Capacitance (Cf)
Frequency droop coefficient (m)
Voltage droop coefficient (n)
3.5 kV
3 kV/11 kV, 0.5 MVA, 2.5%
reactance (Lf)
1.5 Ω
0.0578 H
30 µF
0.005 rad/s/kW
0.2045 kV/kVAr
DG-2
DC voltage (Vdc1)
Transformer rating
VSC losses
Source inductance (L1)
Filter Capacitance (Cf)
Frequency droop coefficient (m)
Voltage droop coefficient (n)
3.5 kV
3 kV/11 kV, 0.5 MVA, 2.5%
reactance (Lf)
1.5 Ω
0.0722 H
30 µF
0.00625 rad/s/kW
0.2727 kV/kVAr
Passive load The load is varied between
4.84 + j30.25 Ω and
102.85 + j157.3 Ω
Motor load (synchronous)
Rated rms voltage (L-N)
Rated rms line current
Inertia constant
Iron loss resistance
6 kV
5 kA
1 s
300 pu
Motor load (induction)
Rated rms voltage (L-N)
Rated rms line current
Rated power
6 kV
0.11 kA
50 hp
3.1.2.2 GRID CONNECTED MODE
In the grid connected mode, the steady state system frequency is fixed to the utility frequency. It is
assumed that the distributed generators supply their rated power at rated frequency. When the load
requirement is less than the total rated power of the DGs, the excess power flows from DGs go to the
33
grid.For a motor load, even a slight transient in voltage causes large power swing. Therefore the PCC
voltage should not deviate much from its nominal value and the VSCs must supply the change in the
power demand as quickly as possible. To accomplish this, relying only on a voltage control may not
be sufficient. It is desirable that a current controller is added with the voltage controller to ensure
better power tracking. Therefore the control is changed to a state feedback control which uses the
feedback of DG output voltage; output current and the current through the filter capacitor (see
Appendix A).
1.8 2 2.2 2.4 2.6 2.8 3 3.2
0
0.5
1
1.5
2
Act
ive
pow
er (
MW
)
1.8 2 2.2 2.4 2.6 2.8 3 3.2-0.6
-0.4
-0.2
0
0.2
0.4
Time (s)
Cur
rent
-pha
se a
(kA
)
DG1DG2Grid
DG1DG2Grid
Fig .3.3. System response with motor load in islanded mode.
The reference voltage magnitude and angle are calculated from the droop similar to the islanded
mode. However the steady state frequency is fixed to the grid frequency and the power output of the
DGs are equal to their rated power. Thus the active and reactive power requirements for an individual
DG are calculated based on their rating. The output current reference is calculated from the power and
voltage reference. The reference for the filter capacitor current is calculated from the voltage reference
(Appendix A).
Fig. 3.4 shows the system response during change of load in the grid connected mode. In this mode,
any change in load is picked up by the grid as the DGs always provide the rated power (or the
maximum available power). The change in grid current with active power demand ensures a stable
operation.
Fig. 3.5 shows the results when an induction motor gets connected at 2 s and disconnected at 2.75 s
while the passive load remains connected all the time. It is obvious that the additional power required
by the motor is coming from the grid as the DGs supply the rated power.
34
Fig. 3.6 shows the results when a synchronous motor is connected in parallel with impedance load.
With the motor and impedance operating in the steady state, the motor is disconnected at 1.5 s and
reconnected at 3 s. It can be seen that the powers supplied by the DGs remain constant during both the
transients and the oscillations in the grid current die out within 1 s.
1.2 1.4 1.6 1.8 2 2.2 2.4-0.5
0
0.5
1
1.5
Act
ive
pow
er (M
W)
1.2 1.4 1.6 1.8 2 2.2 2.4-0.2
-0.1
0
0.1
0.2
Time(s)
Gri
d C
urr
ent -
pha
se a
(kA
)
DG1DG2Grid
Fig. 3.4. System response with impedance load in grid connected mode.
1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.20
1
2
3
Act
ive
pow
er (
MW
)
1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2-0.4
-0.2
0
0.2
0.4
Time(s)
Gri
d c
urr
ent -
pha
se-a
(kA
)
DG1DG2Grid
Fig.3.5. System response with induction motor load in grid connected mode.
3.1.2.3 SEAMLESS TRANSFER BETWEEN GRID CONNECTED AND ISLANDED
MODES
The results simulated so far show that a better load sharing and a quick steady state attainment are
achieved with the voltage control in the islanded mode, while the state feedback ensures better
response in the grid connected mode. A seamless transfer between these two modes is proposed by
changing state feedback to voltage control and vice versa. Ordinarily, in the grid connected mode, the
35
DGs operate under the state feedback control. When an islanding is detected, the DGs are switched to
the voltage control mode. These are switched back to the state feedback control mode after
resynchronization. The sequence of control from a grid connected operation to islanded mode and
then again back to grid connected is given in Fig. 3.7.
1 1.5 2 2.5 3 3.5 4 4.5
0
0.5
1
Act
ive
pow
er (
MW
)
1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3-0.04
-0.02
0
0.02
0.04G
rid
cur
rent
(kA
)
2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4-0.04
-0.02
0
0.02
0.04
Time (s)
Gri
d cu
rren
t(k
A)
DG1DG2Grid
Fig.3.6. System response with synchronous motor load in grid connected mode.
Figs. 3.8 and 3.9 show the response of the system during islanding and resynchronization with the
impedance load. The islanding occurs at 1.5 s and the resynchronization occurs at 2 s. Fig. 3.8 shows
the power sharing and currents, while the PCC voltages are shown in Fig. 3.9.
An impedance load is an infinite sink as it can absorb any change in instantaneous real and reactive
power with a change in the supply voltage. This however is not true for an inertial load such as motor.
Thus any change in the terminal voltage will result in large oscillation in the real and reactive powers.
So damping becomes a major issue during islanding with inertial load. Since the voltage control is a
slow process, a re-initialization in the reference value is required to force the system to a new steady
state quickly.
For this analysis it is assumed that an online load flow study is always performed in background
with the microgrid load and generation. At the instant of islanding, the values obtained from the load
flow are used to determine the new voltage reference. The new reference ensures minimal change in
the load voltage after islanding and proper sharing of the loads among the DGs. These new values are
assigned as the new reference for the controllers.
36
Fig.3.7. Control sequence from a grid connected operation to islanded mode
Fig. 3.8, System response during islanding and resynchronization with impedance load.
37
Fig. 3.9. PCC voltage during islanding and resynchronization with impedance load
Fig. 3.10 shows the active power sharing during islanding and resynchronization with a motor load.
An induction motor is used here. The active power input to the motor load is also shown in this figure.
It can be seen that this power remains constant during islanding and resynchronization, validating a
seamless transfer between the two modes. Phase-a of the DG output currents along with the grid
currents are shown separately during islanding and resynchronization in Fig. 3.11. It can be seen that
all the currents reach their steady state values with 0.2 s, both during islanding and resynchronization.
0.5 1 1.5 2 2.5 3 3.5
0
0.5
1
1.5
2
2.5
Act
ive
pow
er (M
W)
0.5 1 1.5 2 2.5 3 3.50.5
1
1.5
2
2.5
Time (s)
Act
ive
pow
er o
f M
oto
r L
oad
(MW
)
DG1DG2Grid
Fig. 3.10. System response during islanding and resynchronization with motor load.
3.2 MICROGRID WITH INERTIAL AND NON INERTIAL DGS
A microgrid should appear as a single controllable load that responds to changes
in the distribution system. Different micro-sources can be connected to the
microgrid, such as inertial sources like diesel generators and converter interfaced
sources such as fuel cells or photovoltaics (PV). A diesel generator set (genset)
38
consists of an internal combustion (IC) engine and a synchronous generator mounted
on the same shaft. Such systems are widely used as backup or emergency power in
commercial as well as industrial installations. Diesel gensets are also heavily used in
remote locations where it is impractical or prohibitively expensive to connect to
utility power [73]. Over the last few decades, there has been a growing interest in
fuel cell systems for power generation. These has been identified as a suitable
solution for distributed generation [74].
Fig. 3.11. PCC voltage during islanding and resynchronization with motor load.
Other than fuel cell, the use of new efficient photovoltaic solar cells (PVs) has emerged as an
alternative source of renewable green power, energy conservation and demand side management. [75].
To investigate the operation of all the micro-sources together, a microgrid is planned at QUT where
the main issue is decentralized power sharing and system stability. It is desired that in a microgrid all
the DGs respond to any load change in a similar rate to avoid the overloading of a lagging or leading
DG. In the presence of both inertial and non inertial DGs, the response time for each DG to any
change in load power demand will be different. A converter interfaced DG can control its output
voltage instantaneously and so the change in the power demand can be picked up quickly, while in an
inertial DG, the rate of change in power output is limited by the machine inertia. To ensure that a load
change is picked up by all the DGs in same rate, the rate of change in converter interfaced DGs needs
to be limited.
39
3.2.1 SYSTEM STRUCTURE
The microgrid system under consideration is shown in Fig. 3.12. There are four DGs as shown;
one of them is an inertial DG (diesel generator) while the others are converter interfaced DGs (the PV,
fuel cell and battery). There are five resistive heater loads and six induction motors. The parameters of
the grid, DGs, loads and controllers are given in Appendix A. The microgrid can run both in grid
connected, as well as, autonomous mode of operation.
Fig.3.12 Microgrid structure under consideration
To increase the system damping and to restrict the rate of change in power output in non inertial
DGs, the droop equations are modified as
dtdQ
nQQnVV
dtdP
mPPm
drated
drateds
+−−=
+−−=
∗ )(
)(ωω (3.1)
3.2.2 MODEL OF MICRO SOURCE
As mentioned before there are four DGs in the microgrid. The diesel generator is modeled as [73]
and not shown in this chapter. The other three DG models and associated power electronic controllers
are discussed below.
3.2.2.1. FUEL CELL
Various methods have been introduced for modeling of fuel cells; however a simplified empirical
model, introduced in [74], is used here. The output voltage-current characteristic of the fuel cell is
given in (3.2). An open loop boost chopper is used at fuel cell output for regulating the necessary DC
voltage VC across the capacitor. The schematic diagram of the simulated model with the output
As high droop gains are needed for proper load sharing, the proposed supplementary controller is
aimed to guarantee the system stability even with high droop gains. Note that the controller gains were
optimized to obtain a good performance over a range of operating conditions despite the requirement
of stabilizing a family of a number of unstable plants with a fixed structure low order compensator.
This has resulted in the change of frequencies of the dominant eigenvalues. However, as the
frequencies did not migrate either up to the switching range or down to the low oscillatory frequency
range, it was not necessary to modify the performance index to avoid the frequency shift.
110
6.7.1 TEST SYSTEM
The structure of the study system is shown in Fig. 6.14. The real and reactive powers supplied by
the DGs are denoted by Pi, Qi, i = 1, …, 4. The real and reactive power demand from the loads are
denoted by PLi, QLi, i = 1, …, 5. The line impedances are denoted by Z12-Z89 in the figure. The system
matrix AT is derived with all the parameter shown in Table-6.4 for eigenvalue analysis.
Fig. 6.14. Microgrid system under consideration.
6.7.2 SIMULATION STUDIES WITH SUPPLEMENTARY DROOP CONTROLLER Different configurations of load and power sharing of the DGs are considered to ensure that the
propose controller provide a stable operation in all the situations . The DGs are considered as inertia
less dc source supplied through a VSC.
6.7.2.1 CASE 1: FULL SYSTEM OF FIG. 6 WITH LOWER DROOP GAINS
In this case, it is assumed that all the DGs and loads are connected to the microgrid as shown in Fig.
6. The lower droop gains values of controller parameters, given in Table-6.4, are considered here.
With the system operating in the steady state, Ld1 changed to 155 kW from 100 kW at 0.25 s. Fig.
6.15 (a) shows the real power sharing while Fig. 6.15 (b) shows the three phase terminal voltages of
DG-1. It can be seen that the controller provides proper load sharing with stable system operation.
6.7.2.2 CASE 2: REDUCED SYSTEM WITH LOWER DROOP GAINS
To investigate the load sharing with reduced system, DG-2 and DG-3 are disconnected at 0.25 s and
the total power is shared by DG-1 and DG-4 as shown in Fig. 6.16. At 1.3 s, Ld2 Ld3, Ld4 and Ld5 are
also disconnected. The two DGs connected to the microgrid supply the 100 kW load, Ld1. It can be
seen that system operation is stable. However due to weak system condition, as the DGs are located
geographically far from each other, they can not share load in the desired ratio of 1:1.33
111
Fig. 6.15. Real and reactive power during a change in load 1.
Fig. 6.16.Power sharing with reduced system
6.7.2.3. CASE 3: SYSTEM STABILITY WITH HIGH DROOP GAIN
As discussed before, the power sharing can be made independent of the system condition and the
converter output reactance by choosing high droop controller gains. The eigenvalue analysis, on the
other hand, predicted system instability for such gains. To investigated the system stability with high
droop gain, the full system (Case-1) is operated first with lower value of droop gain and at 0.2 s, the
droop gains are changed to higher values as mentioned in Table-I. Fig. 6.17 (a) shows the system
response with only droop controller while Fig. 6.17 (b) shows system response with proposed
supplementary droop controller.
112
Fig. 6.17. System stability with high droop gain.
6.7.2.4. CASE 4: POWER SHARING WITH THE PROPOSED SUPPLEMENTARY CONTROLLER
In this section, we shall investigate the load sharing capability with proposed supplementary
controller and the system stability. All the simulations are done with high droop controller gain as
mentioned in Table-6.4. With the system running in steady state and supplying power to all the loads,
Ld5 is disconnected from the microgrid at 0.25 s. Fig. 6.18 shows the system response. The power
output of all the converters reduces proportionally and system attains steady state within 8-10 cycles.
The droop controller converter output voltage reference angle and supplementary controller d-axis
voltage modulation is shown in Fig. 6.19, which clearly shows a damping type controller with 90°
phase shift during transients.
Fig. 6.18. Power sharing with proposed controller.
113
Fig. 6.19.Droop controller and supplementary controller output.
6.7.2.5. CASE 5: POWER SHARING WITH THE PROPOSED CONTROLLER IN REDUCED SYSTEM
The power sharing with the proposed controller in the reduced system is investigated in this section.
DG-1 is disconnected first at 0.25 s when system is running in steady state. Fig. 6.20 shows the
response and it can be seen that the other three DGs supply the extra power requirement. Ld5 is
disconnected at 1.3 s and the DG outputs reduce proportionally. From the system response and
numerical values (Appendix-A) it can be concluded that the DGs share the loads as desired while
ensuring stable operation of the system.
Fig. 6.20. System response for different system configuration.
To validate the performance of the supplementary proposed controller, the microgrid is operated
similar situation as described in Case 2 with reduced system. Fig. 6.21 shows the system response.